# Trustworthy scientific inference with generative models

arXiv: https://arxiv.org/abs/2508.02602 · HTML: https://mlsanity.com/paper/2508.02602/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 121 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 30 of 40)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Diagnostics for Conditional Density Models and Bayesian Inference Algorithms](https://mlsanity.com/paper/2102.10473/) (2021)
- [Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation](https://mlsanity.com/paper/2208.13624/) (2022)
- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [Fast covariance parameter estimation of spatial Gaussian process models using neural networks](https://mlsanity.com/paper/2012.15339/) (2020)
- [Consistency Models for Scalable and Fast Simulation-Based Inference](https://mlsanity.com/paper/2312.05440/) (2023)
- [Bayes-optimal prediction with frequentist coverage control](https://mlsanity.com/paper/2105.14045/) (2021)
- [Confidence Sets and Hypothesis Testing in a Likelihood-Free Inference Setting](https://mlsanity.com/paper/2002.10399/) (2020)
- [OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany](https://mlsanity.com/paper/2010.00300/) (2020)
- [L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference](https://mlsanity.com/paper/2306.03580/) (2023)
- [Frequentist coverage and sup-norm convergence rate in Gaussian process regression](https://mlsanity.com/paper/1708.04753/) (2017)
- [Simulator-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problems](https://mlsanity.com/paper/2205.15680/) (2022)
- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inference](https://mlsanity.com/paper/2107.03920/) (2021)
- [Towards Instance-Wise Calibration: Local Amortized Diagnostics and Reshaping of Conditional Densities (LADaR)](https://mlsanity.com/paper/2205.14568/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learning the Universe: Posterior Reliability of Neural Generative Models in High-Dimensional Field-Level Inference of Cosmic Initial Conditions](https://mlsanity.com/paper/2606.10023/) (2026)

## Abstract (arXiv)

Generative artificial intelligence (AI) excels at producing complex data structures (text, images, videos) by learning patterns from training examples. Across scientific disciplines, researchers are now applying generative models to "inverse problems" to directly predict hidden parameters from observed data along with measures of uncertainty. While these predictive or posterior-based methods can handle intractable likelihoods and large-scale studies, they can also produce biased or overconfident conclusions even without model misspecifications. We present a solution with Frequentist-Bayes (FreB), a mathematically rigorous protocol that reshapes AI-generated posterior probability distributions into (locally valid) confidence regions that consistently include true parameters with the expected probability, while achieving minimum size when training and target data align. We demonstrate FreB's effectiveness by tackling diverse case studies in the physical sciences: identifying unknown sources under dataset shift, reconciling competing theoretical models, and mitigating selection bias and systematics in observational studies. By providing validity guarantees with interpretable diagnostics, FreB enables trustworthy scientific inference across fields where direct likelihood evaluation remains impossible or prohibitively expensive.